Transitioning from Affinity Designer to Adobe Illustrator

Make sure you only use features that Illustrator fully supports or you might get rasters. So take care of gradients. Brushes can be an issue as well. It depends on your objective. Do you need full vector? Do you need full editability? And is there a feature in Illustrator that allows you to recreate the look of the original. Depending on that you decide if you reset brushes, strokes, gradients to a very basic stroke and/or fill and then export or export as is and just make sure resolution is enough.

You could try copy and paste.

If that does not work, export a PDF that keeps transparency (so no PDF/X 1 or 3). You might need to fiddle around with options.

What you cannot keep are layers. Illustrator doesn't convert "PDF layers" to its own layers as Affinity Designer does.

So you might want to put stuff on different artboards and rebuild the layers from that. Or try groups.

Text will be split in a gazillion text objects. Select all those, copy them, make a new area text and paste.

If you will have to do this repeatedly, try the plugin VectorFirstAid. It helps with several PDF problems.